Demand for wireless digital communication and data processing systems is on the rise. Inherent in most digital communication channels are errors introduced when transferring frames, packets or cells containing data. Such errors are often caused by electrical interference or thermal noise. Data transmission error rates depend, in part, on the medium which carries the data. Typical bit error rates for copper based data transmission systems are in the order of 10−6. Optical fibers have typical bit error rates of 10−9 or less. Wireless transmission systems, on the other hand, may have error rates of 10−3 or higher. The relatively high bit error rates of wireless transmission systems pose certain difficulties in encoding and decoding of data transmitted via such systems. Partly because of its mathematical tractability and partly because of its application to a broad class of physical communication channels, the additive white Gaussian noise (AWGN) model is often used to characterize the noise in most communication channels.
Data is often encoded at the transmitter, in a controlled manner, to include redundancy. The redundancy is subsequently used by the receiver to overcome the noise and interference introduced in the data while being transmitted through the channel. For example, the transmitter might encode k bits with n bits where n is greater than k, according to some coding scheme. The amount of redundancy introduced by the encoding of the data is determined by the ratio n/k, the inverse of which is referred to as the code rate.
To gain bandwidth efficiency and coding, Trellis Coded Modulation (TCM) has been developed and combines a multilevel phase modulation signaling set with a trellis coding scheme. TCM increases the minimum Euclidean distance between pairs of coded signals to reduce the loss from the expansion of signal set and to achieve coding gain with relatively simple codes. Another known technique used to code data is convolutional coding such as the ½ rate convolutional code defined by the 802.11a standard.
At the receiving end of a transmission channel, the coded symbols must be decoded. The Viterbi algorithm is an efficient maximum-likelihood sequence detection method for decoding convolutional and trellis coded symbols transmitted over AWGN channels. In accordance with the Viterbi algorithm, for each received signal, a distance between that signal at time ti and all the trellis paths entering each state at time ti is calculated. In the Viterbi algorithm, the minimum Euclidean distance is selected as the optimum branch metric for decoding convolutional and trellis sequences transmitted in AWGN channels.
In a multiple-input multiple-output (MIMO) system, the transmitter includes multiple transmit antennas and the receiver includes multiple receive antennas. A MIMO system is typically used to increase the data rate, diversity, or a combination thereof. The increase in data rate is achieved by transmitting multiple data streams via the multiple transmit antennas, also known as spatial multiplexing. The diversity is achieved by increasing the redundancy between the transmit antennas through joint coding.